"Establishing this trust and making the initial deposit ahead of schedule further demonstrates our commitment to making it right in the Gulf Coast.”

Kenneth Feinberg will oversee the $20 billion Gulf Coast Claims Fund, and he is expected to set up shop before the end of August.

The cost of the spill has reached $6.1 billion for BP, including response, containment, relief-well drilling, static kill and cementing, grants to the Gulf states, claims paid and federal costs, the company also announced Monday.

BP has said it will continue to make claim payments to individuals and businesses affected by the oil spill until Feinberg takes over.

The oil giant has spent $319 million on more than 103,900 claims, through August 7. About 145,000 claims had been submitted to BP, the company said.

In addition, BP announced two individual trustees have been named to the newly established trust that will administer the account: John Martin, a former U.S. district judge for the Southern District of New York, and Kent Syverud, dean of the Washington University School of Law.

Citigroup will serve as corporate trustee and paying agent for the account. Arrangements have been made for checks drawn on the fund to be cashed free of charge at any of the 160 Whitney National Bank branches across the Gulf Coast region, the company said.